Question

1. a claim is made that 12% of adults do not have a driver’s license. a researcher has reason to believe this claimed value is too high. after surveying a random sample of adults, the researcher observes that 8% of the adults in the sample do not have a driver’s license. the researcher decides to conduct a hypothesis test and writes out the alternative hypothesis as ( h_{a}: p>0.12 ). what is wrong with this?

a. nothing is wrong.
b. the alternative hypothesis should be written as ( h_{a}: p = 0.08 ).
c. the alternative hypothesis should be written as ( h_{a}: p<0.12 ).
d. the alternative hypothesis should be written as ( h_{a}: p>0.08 ).
e. the alternative hypothesis should be written as ( h_{a}: p<12% ).

Explanation:

The researcher believes the claimed value (12%) is too high. In hypothesis testing, the alternative hypothesis \(H_a\) should reflect the researcher's belief. If the claim is \(p = 0.12\) (null hypothesis \(H_0:p = 0.12\)) and the researcher thinks it's too high, the alternative hypothesis should be \(p<0.12\). The sample proportion (\(0.08\)) is just an observed value from the sample, and the hypotheses are about the population proportion \(p\).

Answer:

C. The alternative hypothesis should be written as \(H_a:p < 0.12\).
E. The alternative hypothesis should be written as \(H_a:p < 12\%\) (since \(0.12 = 12\%\)).